00:01
Belongs to the gravitational chapter.
00:01
So, in this question, we have radius of the black hole that is a distance from the black hole center at which escape speed ve becomes the speed of light.
00:11
So for the part a of the question, we have to calculate the radius of the black hole capital r as with the mass twice that of sun.
00:19
So mass of the black hole, this is equals to twice of mass of the sun.
00:24
So radius escape speed ve, it is equals to 2 gm by r.
00:30
Gm by r to gm by capital r so substituting values here so escape speed has become speed of light c and this is equals to 2 gm by r s under root so from here after solving we get r s equals to 2 gm divided by c square this m is the mass of the black hole so we can write mb8.
01:00
So, substituting values, so we get rs equals to 2 modplared by g, which is 6 .674, mudplared by 10 to the power minus 11 newton meter square per kg square.
01:12
Modipared by mass of the black hole, which is twice of the mass of sun.
01:15
So 2 muddplared by mass of sun is 1 .981, muddler by 10 to the power 30 kg divided by speed of the light, which is 2 .998 into 10 to the power 8 meter per second.
01:27
So, whole square.
01:28
So from here after solving radius of the black hole comes out to be, this comes out to be 5 .908 kilometer.
01:39
So this become the answer for the part a of the problem.
01:43
Now moving to the next part in which we have to calculate at what radius from the center of black hole in part a, the orbital speed will be equals to the speed of the light.
01:53
So the orbital speed, v, it is equal to gm by capital.
01:57
R under root.
01:59
So orbital speed has become to the speed of the light...